Abstract
The tanh-type, tan-type, and e-type Hurwitz continued fractions have been generalized by the author. In this paper, we study a generalized form of e2-type Hurwitz continued fractions by using confluent hypergeometric functions. We also obtain a similar type of Tasoev continued fractions.
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A. Châtelet, Contribution a la théorie des fractions continues arithmétiques, Bull. Soc. Math. France, 40, 1–25 (1912).
C. S. Davis, On some simple continued fractions connected with e, J. London Math. Soc., 20, 194–198 (1945).
A. Hurwitz, Über die Kettenbrüche, deren Teilnenner arithmitische Reihen bilden, Vierteljahrsschrift d. Naturforsch, Gesellschaft in Zürich, 41 (1896) = Mathematische Werke, II, Birkhäuser, Basel 276–302 (1963).
T. Komatsu, On Tasoev’s continued fractions, Math. Proc. Cambridge Philos. Soc., 134, 1–12 (2003).
T. Komatsu, On Hurwitzian and Tasoev’s continued fractions, Acta Arith., 107, 161–177 (2003).
T. Komatsu, Tasoev’s continued fractions and Rogers-Ramanujan continued fractions, J. Number Theory, 109, 27–40 (2004).
T. Komatsu, Hurwitz and Tasoev continued fractions, Monatsh. Math., 145, 47–60 (2005).
T. Komatsu, An algorithm of infinite sums representations and Tasoev continued fractions, Math. Comp., 74, 2081–2094 (2005).
O. Perron, Die Lehre von den Kettenbru \(\ddot c\) hen, Band I, Teubner, Stüttgart (1954).
G. N. Raney, On continued fractions and finite automata, Math. Ann., 206, 265–283 (1973).
L. J. Slater, Generalized Hypergeometric Functions, Cambridge Univ. Press, Cambridge (1966).
B. G. Tasoev, Rational approximations to certain numbers, Mat. Zametki, 67, 931–937 (2000); English transl. in Math. Notes, 67, 786–791 (2000).
R. F. C. Walters, Alternative derivation of some regular continued fractions, J. Austral. Math. Soc., 8, 205–212 (1968).
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Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 4, pp. 513–531, October–December, 2006.
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Komatsu, T. Continued fraction of e2 with confluent hypergeometric functions. Lith Math J 46, 417–431 (2006). https://doi.org/10.1007/s10986-006-0039-6
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DOI: https://doi.org/10.1007/s10986-006-0039-6